Question

exponential growth functions
when initially observed, a jellyfish population is 240. the population of jellyfish grows exponentially at a rate of 14% each year. write an exponential growth function to model the jellyfish population. let the variable x represent the number of years since the jellyfish population was initially observed. let f(x) represent the number of jellyfish in the population after x years.
enter your answer in the box.
f(x) = \square

Explanation:

Step1: Recall Exponential Growth Formula

The general formula for exponential growth is \( f(x) = a(1 + r)^x \), where \( a \) is the initial amount, \( r \) is the growth rate (in decimal), and \( x \) is the time.

Step2: Identify Values for \( a \) and \( r \)

Here, the initial population \( a = 240 \), and the growth rate \( r = 14\% = 0.14 \).

Step3: Substitute Values into Formula

Substitute \( a = 240 \) and \( r = 0.14 \) into the formula: \( f(x) = 240(1 + 0.14)^x = 240(1.14)^x \).

Answer:

\( 240(1.14)^x \)